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    "headline": "A Public Projection Removed Randomness From the Proof Circuit",
    "slug": "a-public-projection-removed-randomness-from-the-proof-circuit",
    "dek": "A deterministic Pisot-based projection preserved semantic distances without sampling a matrix inside the zero-knowledge circuit.",
    "summary": "A deterministic Pisot-based projection preserved semantic distances without sampling a matrix inside the zero-knowledge circuit.",
    "body_text": "The construction matches six comparison projections within measurement noise and is exactly reproducible in a fixed finite field. One dimension-free concentration result remains conditional on a stated hypothesis.",
    "why_it_matters": "A deterministic Pisot-based projection preserved semantic distances without sampling a matrix inside the zero-knowledge circuit.",
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      "dimensionality reduction"
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      "title": "arXiv preprint 2608.13078",
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    "title": "A Public Projection Removed Randomness From the Proof Circuit",
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